No, too many parks is just as bad as too many parking lots, for the same reason: they force the city to sprawl. A few parks are good - and the exact amount is debatable, but the proposal to turn all parking lots into parks will create too many parks.

Everyone should have a park close to where they live. A place where kids can play and families can picnic is important to a good family life. A park is a good place for art, but it only needs to be accessible by transit as most people won't make regular visits. Many people enjoy playing volleyball, softball, or other sports, but they tend to want to play different teams so while a city should have this it should be accessible by transit but not close to everyone. There are a few variations on the above theme that I didn't mention. Once those uses are covered a city should not build more parks, instead the city needs more of the other things that make a city: places to live, work, shop, and be entertained.